The breakdown of the reciprocity relation between the right-handed (\(\eta >0\) ) and left-handed (\(\eta <0\) ) elliptically polarized electric fields obtained in this work can be understood in terms of symmetry reduction of the crystal structure.
The external shear strain changes the crystal structure of GaAs from cubic (zinc blende structure) into monoclinic, inducing off-diagonal elements in the dielectric tensor \(\epsilon _{zx}\)[1]}, [2]}.
The emergence of \(\epsilon _{zx}\)  directly means optical activity, i.e., different responses to left-handed and right-handed elliptically polarized electric fields. It should be noted that the breakdown in reciprocity becomes rather pronounced when the emitted photon energy exceeds the band-gap energy, which is \(E_{g} = 7\hbar \omega _{0}\)  in our calculation.
The origin of this feature is conjectured to be as follows.
When the emitted photon energy is larger than the band-gap energy, the number of excitation channels relevant to HHG largely increases in comparison with those for the low-order harmonics below the band-gap energy.
The increase in the available channels contributes to emergence of the plateau structure in the HHG spectra[3]}, as well as oscillatory behavior as a function of field strength[4]}.
Thus, we suppose that the sensitivity of the high-order harmonics above the band-gap energy to the external strain effect is caused by an increase in the excitation channels.
This breakdown of reciprocity in HHG that is sensitive to shear strain may be used for applications such as spatially-resolved measurement of lattice deformation.
The features revealed here may also be useful for developing a mechanical control of HHG ellipticity.
